Pre-announced posted pricing scheme: Existence and uniqueness of equilibrium bidding strategy

We scrutinize the uniqueness issue of the equilibrium behavior of strategic customers making inter-temporal purchase decisions. We present that multiple equilibria can exist even in the simple setting where two identical customers compete for one unit of item. We prove the existence of a unique symmetric equilibrium when there are no more than three buyers whose valuations follow a uniform distribution. When there are multiple equilibria we show that the bidding strategy having the biggest threshold is Pareto-optimal for buyers.